def test_rand(self):
# Just make sure that things generated are on the manifold and that
# if you generate two they are not equal.
X = self.man.rand()
np_testing.assert_allclose(multiprod(multihconj(X), X),
multieye(self.k, self.n), atol=1e-10)
Y = self.man.rand()
assert la.norm(X - Y) > 1e-6
assert np.iscomplex(X).all()
def test_randvec(self):
# Make sure things generated are in tangent space and if you generate
# two then they are not equal.
X = self.man.rand()
U = self.man.randvec(X)
np_testing.assert_allclose(multisym(multiprod(multihconj(X), U)),
np.zeros((self.k, self.n, self.n)),
atol=1e-10)
V = self.man.randvec(X)
assert la.norm(U - V) > 1e-6
assert np.iscomplex(U).all()
def test_random_point(self):
# Just make sure that things generated are on the manifold
# and that if you generate two they are not equal.
# Test also that matrices are complex.
X = self.manifold.random_point()
np_testing.assert_allclose(multihconj(X) @ X,
np.eye(self.n),
atol=1e-10)
Y = self.manifold.random_point()
assert np.linalg.norm(X - Y) > 1e-6
assert np.iscomplex(X).all()
def test_randvec(self):
# Just make sure that things generated are on the horizontal space of
# complex Stiefel manifold
# and that if you generate two they are not equal.
# Test also that matrices are complex.
X = self.man.rand()
G = self.man.randvec(X)
np_testing.assert_allclose(multiprod(multihconj(X), G),
np.zeros((self.n, self.n)), atol=1e-10)
H = self.man.randvec(X)
assert la.norm(G - H) > 1e-6
assert np.iscomplex(G).all()
def test_unimplemented_falseyness():
@contextmanager
def remove_grad_definitions(fun):
vjpmaker = primitive_vjps.pop(fun, None)
yield
if vjpmaker:
primitive_vjps[fun] = vjpmaker
with remove_grad_definitions(np.iscomplex):
fun = lambda x: np.real(x**2 if np.iscomplex(x) else np.sum(x))
check_grads(fun)(5.)
check_grads(fun)(2. + 1j)
def test_unimplemented_falseyness():
@contextmanager
def remove_grad_definitions(fun):
vjpmaker = primitive_vjps.pop(fun, None)
yield
if vjpmaker:
primitive_vjps[fun] = vjpmaker
with remove_grad_definitions(np.iscomplex):
fun = lambda x: np.real(x**2 if np.iscomplex(x) else np.sum(x))
check_grads(fun)(5.)
check_grads(fun)(2. + 1j)
def test_random_tangent_vector(self):
# Make sure things generated are in tangent space and if you generate
# two then they are not equal.
X = self.manifold.random_point()
U = self.manifold.random_tangent_vector(X)
np_testing.assert_allclose(
multisym(multihconj(X) @ U),
np.zeros((self.k, self.n, self.n)),
atol=1e-10,
)
V = self.manifold.random_tangent_vector(X)
assert np.linalg.norm(U - V) > 1e-6
assert np.iscomplex(U).all()
def test_unimplemented_falseyness():
def remove_grad_definitions(fun):
return primitive_vjps.pop(fun, None)
def restore_grad_definitions(fun, grads):
if grads:
primitive_vjps[fun] = grads
grad_defs = remove_grad_definitions(np.iscomplex)
fun = lambda x: np.real(x**2 if np.iscomplex(x) else np.sum(x))
check_grads(fun)(5.)
check_grads(fun)(2. + 1j)
restore_grad_definitions(np.iscomplex, grad_defs)
def test_unimplemented_falseyness():
def remove_grad_definitions(fun):
grads, zero_vjps = fun.vjps, fun.zero_vjps
fun.vjps, fun.zero_vjps = {}, set()
return grads, zero_vjps
def restore_grad_definitions(fun, grad_defs):
fun.vjps, fun.zero_vjps = grad_defs
grad_defs = remove_grad_definitions(np.iscomplex)
fun = lambda x: x**2 if np.iscomplex(x) else np.sum(x)
check_grads(fun, 5.)
check_grads(fun, 2. + 1j)
restore_grad_definitions(np.iscomplex, grad_defs)
def test_unimplemented_falseyness():
def remove_grad_definitions(fun):
grads, zero_vjps = fun.vjps, fun.zero_vjps
fun.vjps, fun.zero_vjps = {}, set()
return grads, zero_vjps
def restore_grad_definitions(fun, grad_defs):
fun.vjps, fun.zero_vjps = grad_defs
grad_defs = remove_grad_definitions(np.iscomplex)
fun = lambda x: x**2 if np.iscomplex(x) else np.sum(x)
check_grads(fun, 5.)
check_grads(fun, 2. + 1j)
restore_grad_definitions(np.iscomplex, grad_defs)
def unary_nd(f, x, eps=1e-4):
if isinstance(x, np.ndarray):
if np.iscomplexobj(x):
nd_grad = np.zeros(x.shape) + 0j
else:
nd_grad = np.zeros(x.shape)
for dims in it.product(*map(range, x.shape)):
nd_grad[dims] = unary_nd(indexed_function(f, x, dims), x[dims])
return nd_grad
elif isinstance(x, tuple):
return tuple([unary_nd(indexed_function(f, tuple(x), i), x[i])
for i in range(len(x))])
elif isinstance(x, dict):
return {k : unary_nd(indexed_function(f, x, k), v) for k, v in x.iteritems()}
elif isinstance(x, list):
return [unary_nd(indexed_function(f, x, i), v) for i, v in enumerate(x)]
elif np.iscomplex(x):
result = (f(x + eps/2) - f(x - eps/2)) / eps \
- 1j*(f(x + 1j*eps/2) - f(x - 1j*eps/2)) / eps
return type(safe_type(x))(result)
else:
return type(safe_type(x))((f(x + eps/2) - f(x - eps/2)) / eps)
def test_falseyness():
fun = lambda x: np.real(x**2 if np.iscomplex(x) else np.sum(x))
check_grads(fun)(2.)
check_grads(fun)(2. + 1j)
def test_falseyness():
fun = lambda x: np.real(x**2 if np.iscomplex(x) else np.sum(x))
check_grads(fun)(2.)
check_grads(fun)(2. + 1j)
def test_falseyness():
fun = lambda x: x**2 if np.iscomplex(x) else np.sum(x)
check_grads(fun, 2.)
check_grads(fun, 2. + 1j)
def test_falseyness():
fun = lambda x: x**2 if np.iscomplex(x) else np.sum(x)
check_grads(fun, 2.)
check_grads(fun, 2. + 1j)